[en] We introduce a generalization of Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of times a word appears as a subsequence of another finite word. Similarly to the Sierpiński gasket that can be built as the limit set, for the Hausdorff distance, of a convergent sequence of normalized compact blocks extracted from Pascal triangle modulo 2, we describe and study the first properties of the subset of [0, 1] × [0, 1] associated with this extended Pascal triangle modulo a prime p.
Disciplines :
Mathématiques
Auteur, co-auteur :
Leroy, Julien ; Université de Liège > Département de mathématique > Mathématiques discrètes
Rigo, Michel ; Université de Liège > Département de mathématique > Mathématiques discrètes
Stipulanti, Manon ; Université de Liège > Département de mathématique > Mathématiques discrètes
Langue du document :
Anglais
Titre :
Generalized Pascal triangle for binomial coefficients of words